﻿using System;
using Lockstep.Math;

namespace Lockstep.Math
{
    public static class LUTAtan2
    {
        public static readonly int BITS;

        public static readonly int BITS2;

        public static readonly int MASK;

        public static readonly int COUNT;

        public static readonly int DIM;

        public static readonly int[] table;

        static LUTAtan2()
        {
            BITS = 7;
            BITS2 = BITS << 1;
            MASK = ~(-1 << BITS2);
            COUNT = MASK + 1;
            DIM = LMath.Sqrt((long) COUNT);
            table = new int[]
            {
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                0,
                15708,
                7854,
                4636,
                3218,
                2450,
                1974,
                1651,
                1419,
                1244,
                1107,
                997,
                907,
                831,
                768,
                713,
                666,
                624,
                588,
                555,
                526,
                500,
                476,
                454,
                435,
                416,
                400,
                384,
                370,
                357,
                345,
                333,
                322,
                312,
                303,
                294,
                286,
                278,
                270,
                263,
                256,
                250,
                244,
                238,
                233,
                227,
                222,
                217,
                213,
                208,
                204,
                200,
                196,
                192,
                189,
                185,
                182,
                179,
                175,
                172,
                169,
                167,
                164,
                161,
                159,
                156,
                154,
                152,
                149,
                147,
                145,
                143,
                141,
                139,
                137,
                135,
                133,
                132,
                130,
                128,
                127,
                125,
                123,
                122,
                120,
                119,
                118,
                116,
                115,
                114,
                112,
                111,
                110,
                109,
                108,
                106,
                105,
                104,
                103,
                102,
                101,
                100,
                99,
                98,
                97,
                96,
                95,
                94,
                93,
                93,
                92,
                91,
                90,
                89,
                88,
                88,
                87,
                86,
                85,
                85,
                84,
                83,
                83,
                82,
                81,
                81,
                80,
                79,
                79,
                15708,
                11071,
                7854,
                5880,
                4636,
                3805,
                3218,
                2783,
                2450,
                2187,
                1974,
                1799,
                1651,
                1526,
                1419,
                1326,
                1244,
                1171,
                1107,
                1049,
                997,
                950,
                907,
                867,
                831,
                798,
                768,
                739,
                713,
                689,
                666,
                644,
                624,
                605,
                588,
                571,
                555,
                540,
                526,
                512,
                500,
                487,
                476,
                465,
                454,
                444,
                435,
                425,
                416,
                408,
                400,
                392,
                384,
                377,
                370,
                363,
                357,
                351,
                345,
                339,
                333,
                328,
                322,
                317,
                312,
                308,
                303,
                298,
                294,
                290,
                286,
                282,
                278,
                274,
                270,
                267,
                263,
                260,
                256,
                253,
                250,
                247,
                244,
                241,
                238,
                235,
                233,
                230,
                227,
                225,
                222,
                220,
                217,
                215,
                213,
                210,
                208,
                206,
                204,
                202,
                200,
                198,
                196,
                194,
                192,
                190,
                189,
                187,
                185,
                183,
                182,
                180,
                179,
                177,
                175,
                174,
                172,
                171,
                169,
                168,
                167,
                165,
                164,
                163,
                161,
                160,
                159,
                157,
                15708,
                12490,
                9828,
                7854,
                6435,
                5404,
                4636,
                4049,
                3588,
                3218,
                2915,
                2663,
                2450,
                2268,
                2111,
                1974,
                1853,
                1747,
                1651,
                1566,
                1489,
                1419,
                1355,
                1297,
                1244,
                1194,
                1149,
                1107,
                1067,
                1031,
                997,
                965,
                935,
                907,
                880,
                855,
                831,
                809,
                788,
                768,
                749,
                730,
                713,
                697,
                681,
                666,
                651,
                637,
                624,
                611,
                599,
                588,
                576,
                565,
                555,
                545,
                535,
                526,
                517,
                508,
                500,
                491,
                483,
                476,
                468,
                461,
                454,
                447,
                441,
                435,
                428,
                422,
                416,
                411,
                405,
                400,
                395,
                389,
                384,
                380,
                375,
                370,
                366,
                361,
                357,
                353,
                349,
                345,
                341,
                337,
                333,
                330,
                326,
                322,
                319,
                316,
                312,
                309,
                306,
                303,
                300,
                297,
                294,
                291,
                288,
                286,
                283,
                280,
                278,
                275,
                273,
                270,
                268,
                265,
                263,
                261,
                259,
                256,
                254,
                252,
                250,
                248,
                246,
                244,
                242,
                240,
                238,
                236,
                15708,
                13258,
                11071,
                9273,
                7854,
                6747,
                5880,
                5191,
                4636,
                4182,
                3805,
                3488,
                3218,
                2985,
                2783,
                2606,
                2450,
                2311,
                2187,
                2075,
                1974,
                1882,
                1799,
                1722,
                1651,
                1587,
                1526,
                1471,
                1419,
                1371,
                1326,
                1283,
                1244,
                1206,
                1171,
                1138,
                1107,
                1077,
                1049,
                1022,
                997,
                973,
                950,
                928,
                907,
                887,
                867,
                849,
                831,
                815,
                798,
                783,
                768,
                753,
                739,
                726,
                713,
                701,
                689,
                677,
                666,
                655,
                644,
                634,
                624,
                615,
                605,
                596,
                588,
                579,
                571,
                563,
                555,
                547,
                540,
                533,
                526,
                519,
                512,
                506,
                500,
                493,
                487,
                482,
                476,
                470,
                465,
                459,
                454,
                449,
                444,
                439,
                435,
                430,
                425,
                421,
                416,
                412,
                408,
                404,
                400,
                396,
                392,
                388,
                384,
                381,
                377,
                374,
                370,
                367,
                363,
                360,
                357,
                354,
                351,
                348,
                345,
                342,
                339,
                336,
                333,
                330,
                328,
                325,
                322,
                320,
                317,
                315,
                15708,
                13734,
                11903,
                10304,
                8961,
                7854,
                6947,
                6202,
                5586,
                5071,
                4636,
                4266,
                3948,
                3672,
                3430,
                3218,
                3029,
                2861,
                2709,
                2573,
                2450,
                2337,
                2235,
                2141,
                2054,
                1974,
                1900,
                1831,
                1767,
                1707,
                1651,
                1599,
                1550,
                1504,
                1460,
                1419,
                1380,
                1343,
                1308,
                1275,
                1244,
                1214,
                1185,
                1158,
                1132,
                1107,
                1083,
                1060,
                1038,
                1017,
                997,
                977,
                959,
                941,
                923,
                907,
                890,
                875,
                860,
                845,
                831,
                818,
                805,
                792,
                780,
                768,
                756,
                745,
                734,
                723,
                713,
                703,
                693,
                684,
                675,
                666,
                657,
                648,
                640,
                632,
                624,
                617,
                609,
                602,
                595,
                588,
                581,
                574,
                568,
                561,
                555,
                549,
                543,
                537,
                531,
                526,
                520,
                515,
                510,
                505,
                500,
                495,
                490,
                485,
                480,
                476,
                471,
                467,
                463,
                458,
                454,
                450,
                446,
                442,
                438,
                435,
                431,
                427,
                423,
                420,
                416,
                413,
                410,
                406,
                403,
                400,
                397,
                393,
                15708,
                14056,
                12490,
                11071,
                9828,
                8761,
                7854,
                7086,
                6435,
                5880,
                5404,
                4993,
                4636,
                4324,
                4049,
                3805,
                3588,
                3393,
                3218,
                3059,
                2915,
                2783,
                2663,
                2552,
                2450,
                2355,
                2268,
                2187,
                2111,
                2040,
                1974,
                1912,
                1853,
                1799,
                1747,
                1698,
                1651,
                1608,
                1566,
                1526,
                1489,
                1453,
                1419,
                1386,
                1355,
                1326,
                1297,
                1270,
                1244,
                1218,
                1194,
                1171,
                1149,
                1127,
                1107,
                1087,
                1067,
                1049,
                1031,
                1013,
                997,
                980,
                965,
                950,
                935,
                920,
                907,
                893,
                880,
                867,
                855,
                843,
                831,
                820,
                809,
                798,
                788,
                778,
                768,
                758,
                749,
                739,
                730,
                722,
                713,
                705,
                697,
                689,
                681,
                673,
                666,
                658,
                651,
                644,
                637,
                631,
                624,
                618,
                611,
                605,
                599,
                593,
                588,
                582,
                576,
                571,
                565,
                560,
                555,
                550,
                545,
                540,
                535,
                530,
                526,
                521,
                517,
                512,
                508,
                504,
                500,
                495,
                491,
                487,
                483,
                480,
                476,
                472,
                15708,
                14289,
                12925,
                11659,
                10517,
                9505,
                8622,
                7854,
                7188,
                6610,
                6107,
                5667,
                5281,
                4939,
                4636,
                4366,
                4124,
                3906,
                3709,
                3530,
                3367,
                3218,
                3081,
                2954,
                2838,
                2730,
                2630,
                2537,
                2450,
                2368,
                2292,
                2221,
                2154,
                2090,
                2030,
                1974,
                1920,
                1870,
                1822,
                1776,
                1732,
                1691,
                1651,
                1614,
                1578,
                1543,
                1510,
                1478,
                1448,
                1419,
                1391,
                1364,
                1338,
                1313,
                1289,
                1266,
                1244,
                1222,
                1201,
                1181,
                1161,
                1143,
                1124,
                1107,
                1089,
                1073,
                1057,
                1041,
                1026,
                1011,
                997,
                983,
                969,
                956,
                943,
                931,
                918,
                907,
                895,
                884,
                873,
                862,
                852,
                841,
                831,
                822,
                812,
                803,
                794,
                785,
                776,
                768,
                759,
                751,
                743,
                736,
                728,
                720,
                713,
                706,
                699,
                692,
                685,
                679,
                672,
                666,
                659,
                653,
                647,
                641,
                636,
                630,
                624,
                619,
                613,
                608,
                603,
                598,
                593,
                588,
                583,
                578,
                573,
                568,
                564,
                559,
                555,
                551,
                15708,
                14464,
                13258,
                12120,
                11071,
                10122,
                9273,
                8520,
                7854,
                7266,
                6747,
                6288,
                5880,
                5517,
                5191,
                4900,
                4636,
                4398,
                4182,
                3985,
                3805,
                3640,
                3488,
                3347,
                3218,
                3097,
                2985,
                2881,
                2783,
                2692,
                2606,
                2526,
                2450,
                2378,
                2311,
                2247,
                2187,
                2129,
                2075,
                2023,
                1974,
                1927,
                1882,
                1839,
                1799,
                1759,
                1722,
                1686,
                1651,
                1618,
                1587,
                1556,
                1526,
                1498,
                1471,
                1444,
                1419,
                1394,
                1371,
                1348,
                1326,
                1304,
                1283,
                1263,
                1244,
                1225,
                1206,
                1188,
                1171,
                1154,
                1138,
                1122,
                1107,
                1092,
                1077,
                1063,
                1049,
                1035,
                1022,
                1009,
                997,
                984,
                973,
                961,
                950,
                938,
                928,
                917,
                907,
                896,
                887,
                877,
                867,
                858,
                849,
                840,
                831,
                823,
                815,
                806,
                798,
                790,
                783,
                775,
                768,
                760,
                753,
                746,
                739,
                733,
                726,
                719,
                713,
                707,
                701,
                695,
                689,
                683,
                677,
                671,
                666,
                660,
                655,
                649,
                644,
                639,
                634,
                629,
                15708,
                14601,
                13521,
                12490,
                11526,
                10637,
                9828,
                9098,
                8442,
                7854,
                7328,
                6857,
                6435,
                6055,
                5713,
                5404,
                5124,
                4869,
                4636,
                4424,
                4229,
                4049,
                3883,
                3730,
                3588,
                3456,
                3332,
                3218,
                3110,
                3009,
                2915,
                2826,
                2742,
                2663,
                2588,
                2517,
                2450,
                2386,
                2326,
                2268,
                2213,
                2161,
                2111,
                2063,
                2018,
                1974,
                1932,
                1892,
                1853,
                1816,
                1781,
                1747,
                1714,
                1682,
                1651,
                1622,
                1594,
                1566,
                1539,
                1514,
                1489,
                1465,
                1442,
                1419,
                1397,
                1376,
                1355,
                1335,
                1316,
                1297,
                1279,
                1261,
                1244,
                1227,
                1210,
                1194,
                1179,
                1164,
                1149,
                1134,
                1120,
                1107,
                1093,
                1080,
                1067,
                1055,
                1043,
                1031,
                1019,
                1008,
                997,
                986,
                975,
                965,
                955,
                945,
                935,
                925,
                916,
                907,
                898,
                889,
                880,
                872,
                863,
                855,
                847,
                839,
                831,
                824,
                816,
                809,
                802,
                795,
                788,
                781,
                774,
                768,
                761,
                755,
                749,
                742,
                736,
                730,
                725,
                719,
                713,
                707,
                15708,
                14711,
                13734,
                12793,
                11903,
                11071,
                10304,
                9601,
                8961,
                8380,
                7854,
                7378,
                6947,
                6557,
                6202,
                5880,
                5586,
                5317,
                5071,
                4845,
                4636,
                4444,
                4266,
                4101,
                3948,
                3805,
                3672,
                3547,
                3430,
                3321,
                3218,
                3120,
                3029,
                2942,
                2861,
                2783,
                2709,
                2640,
                2573,
                2510,
                2450,
                2392,
                2337,
                2285,
                2235,
                2187,
                2141,
                2096,
                2054,
                2013,
                1974,
                1936,
                1900,
                1865,
                1831,
                1799,
                1767,
                1737,
                1707,
                1679,
                1651,
                1625,
                1599,
                1574,
                1550,
                1526,
                1504,
                1482,
                1460,
                1439,
                1419,
                1399,
                1380,
                1361,
                1343,
                1326,
                1308,
                1291,
                1275,
                1259,
                1244,
                1228,
                1214,
                1199,
                1185,
                1171,
                1158,
                1144,
                1132,
                1119,
                1107,
                1095,
                1083,
                1071,
                1060,
                1049,
                1038,
                1027,
                1017,
                1007,
                997,
                987,
                977,
                968,
                959,
                950,
                941,
                932,
                923,
                915,
                907,
                898,
                890,
                883,
                875,
                867,
                860,
                853,
                845,
                838,
                831,
                825,
                818,
                811,
                805,
                798,
                792,
                786,
                15708,
                14801,
                13909,
                13045,
                12220,
                11442,
                10714,
                10041,
                9420,
                8851,
                8330,
                7854,
                7419,
                7023,
                6660,
                6327,
                6023,
                5743,
                5485,
                5248,
                5028,
                4825,
                4636,
                4461,
                4298,
                4145,
                4002,
                3869,
                3743,
                3625,
                3514,
                3410,
                3311,
                3218,
                3129,
                3045,
                2965,
                2890,
                2818,
                2749,
                2684,
                2621,
                2562,
                2504,
                2450,
                2397,
                2347,
                2299,
                2253,
                2208,
                2166,
                2124,
                2085,
                2046,
                2010,
                1974,
                1940,
                1906,
                1874,
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                1216,
                1203,
                1190,
                1177,
                1165,
                1153,
                1141,
                1129,
                1118,
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                1085,
                1074,
                1064,
                1054,
                1044,
                1034,
                1024,
                1015,
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                970,
                962,
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                945,
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                930,
                922,
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                2721,
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                2552,
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                2402,
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                1326,
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                1127,
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                1107,
                1097,
                1087,
                1077,
                1067,
                1058,
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                1040,
                1031,
                1022,
                1013,
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                4214,
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                3971,
                3859,
                3753,
                3652,
                3556,
                3465,
                3379,
                3296,
                3218,
                3142,
                3070,
                3002,
                2936,
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                2812,
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                2593,
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                2450,
                2405,
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                2321,
                2281,
                2242,
                2205,
                2169,
                2134,
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                2067,
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                1889,
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                1554,
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                1518,
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                1346,
                1332,
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                1306,
                1293,
                1280,
                1268,
                1255,
                1244,
                1232,
                1220,
                1209,
                1198,
                1187,
                1176,
                1166,
                1156,
                1145,
                1135,
                1126,
                1116,
                1107,
                1097,
                1088,
                1079,
                1070,
                1062,
                1053,
                1045,
                1036,
                1028,
                1020,
                15708,
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                14289,
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                4498,
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                4124,
                4012,
                3906,
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                3709,
                3617,
                3530,
                3446,
                3367,
                3290,
                3218,
                3148,
                3081,
                3016,
                2954,
                2895,
                2838,
                2783,
                2730,
                2679,
                2630,
                2583,
                2537,
                2493,
                2450,
                2408,
                2368,
                2330,
                2292,
                2256,
                2221,
                2187,
                2154,
                2121,
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                1895,
                1870,
                1845,
                1822,
                1799,
                1776,
                1754,
                1732,
                1711,
                1691,
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                1651,
                1632,
                1614,
                1596,
                1578,
                1560,
                1543,
                1526,
                1510,
                1494,
                1478,
                1463,
                1448,
                1433,
                1419,
                1405,
                1391,
                1377,
                1364,
                1351,
                1338,
                1326,
                1313,
                1301,
                1289,
                1277,
                1266,
                1255,
                1244,
                1233,
                1222,
                1211,
                1201,
                1191,
                1181,
                1171,
                1161,
                1152,
                1143,
                1133,
                1124,
                1115,
                1107,
                1098,
                15708,
                15042,
                14382,
                13734,
                13102,
                12490,
                11903,
                11342,
                10808,
                10304,
                9828,
                9380,
                8961,
                8567,
                8199,
                7854,
                7532,
                7230,
                6947,
                6683,
                6435,
                6202,
                5984,
                5779,
                5586,
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                5233,
                5071,
                4918,
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                4636,
                4507,
                4383,
                4266,
                4155,
                4049,
                3948,
                3852,
                3760,
                3672,
                3588,
                3507,
                3430,
                3356,
                3286,
                3218,
                3152,
                3089,
                3029,
                2971,
                2915,
                2861,
                2808,
                2758,
                2709,
                2663,
                2617,
                2573,
                2531,
                2490,
                2450,
                2411,
                2374,
                2337,
                2302,
                2268,
                2235,
                2202,
                2171,
                2141,
                2111,
                2082,
                2054,
                2027,
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                1924,
                1900,
                1876,
                1853,
                1831,
                1809,
                1788,
                1767,
                1747,
                1727,
                1707,
                1688,
                1670,
                1651,
                1634,
                1616,
                1599,
                1582,
                1566,
                1550,
                1534,
                1519,
                1504,
                1489,
                1474,
                1460,
                1446,
                1432,
                1419,
                1406,
                1393,
                1380,
                1368,
                1355,
                1343,
                1331,
                1320,
                1308,
                1297,
                1286,
                1275,
                1264,
                1254,
                1244,
                1233,
                1223,
                1214,
                1204,
                1194,
                1185,
                1176,
                15708,
                15084,
                14464,
                13854,
                13258,
                12679,
                12120,
                11584,
                11071,
                10584,
                10122,
                9685,
                9273,
                8885,
                8520,
                8176,
                7854,
                7551,
                7266,
                6999,
                6747,
                6511,
                6288,
                6078,
                5880,
                5693,
                5517,
                5350,
                5191,
                5042,
                4900,
                4765,
                4636,
                4515,
                4398,
                4288,
                4182,
                4081,
                3985,
                3893,
                3805,
                3721,
                3640,
                3562,
                3488,
                3416,
                3347,
                3281,
                3218,
                3156,
                3097,
                3040,
                2985,
                2932,
                2881,
                2831,
                2783,
                2737,
                2692,
                2648,
                2606,
                2565,
                2526,
                2487,
                2450,
                2414,
                2378,
                2344,
                2311,
                2279,
                2247,
                2216,
                2187,
                2158,
                2129,
                2102,
                2075,
                2049,
                2023,
                1998,
                1974,
                1950,
                1927,
                1904,
                1882,
                1861,
                1839,
                1819,
                1799,
                1779,
                1759,
                1740,
                1722,
                1704,
                1686,
                1669,
                1651,
                1635,
                1618,
                1602,
                1587,
                1571,
                1556,
                1541,
                1526,
                1512,
                1498,
                1484,
                1471,
                1457,
                1444,
                1432,
                1419,
                1407,
                1394,
                1382,
                1371,
                1359,
                1348,
                1337,
                1326,
                1315,
                1304,
                1294,
                1283,
                1273,
                1263,
                1253,
                15708,
                15120,
                14537,
                13961,
                13397,
                12847,
                12315,
                11802,
                11310,
                10839,
                10391,
                9965,
                9561,
                9179,
                8819,
                8478,
                8157,
                7854,
                7568,
                7299,
                7045,
                6805,
                6579,
                6365,
                6163,
                5972,
                5791,
                5619,
                5457,
                5302,
                5155,
                5016,
                4883,
                4757,
                4636,
                4522,
                4412,
                4307,
                4207,
                4111,
                4019,
                3931,
                3846,
                3765,
                3687,
                3612,
                3540,
                3471,
                3404,
                3339,
                3277,
                3218,
                3160,
                3104,
                3050,
                2998,
                2947,
                2898,
                2851,
                2805,
                2761,
                2718,
                2676,
                2636,
                2596,
                2558,
                2521,
                2485,
                2450,
                2416,
                2382,
                2350,
                2319,
                2288,
                2258,
                2229,
                2201,
                2173,
                2146,
                2120,
                2094,
                2069,
                2044,
                2020,
                1997,
                1974,
                1952,
                1930,
                1908,
                1887,
                1867,
                1847,
                1827,
                1808,
                1789,
                1771,
                1753,
                1735,
                1718,
                1701,
                1684,
                1668,
                1651,
                1636,
                1620,
                1605,
                1590,
                1576,
                1561,
                1547,
                1533,
                1520,
                1506,
                1493,
                1480,
                1468,
                1455,
                1443,
                1431,
                1419,
                1407,
                1396,
                1385,
                1373,
                1362,
                1352,
                1341,
                1331,
                15708,
                15153,
                14601,
                14056,
                13521,
                12998,
                12490,
                11999,
                11526,
                11071,
                10637,
                10222,
                9828,
                9453,
                9098,
                8761,
                8442,
                8140,
                7854,
                7584,
                7328,
                7086,
                6857,
                6640,
                6435,
                6240,
                6055,
                5880,
                5713,
                5555,
                5404,
                5261,
                5124,
                4993,
                4869,
                4750,
                4636,
                4528,
                4424,
                4324,
                4229,
                4137,
                4049,
                3964,
                3883,
                3805,
                3730,
                3657,
                3588,
                3520,
                3456,
                3393,
                3332,
                3274,
                3218,
                3163,
                3110,
                3059,
                3009,
                2961,
                2915,
                2869,
                2826,
                2783,
                2742,
                2702,
                2663,
                2625,
                2588,
                2552,
                2517,
                2483,
                2450,
                2418,
                2386,
                2355,
                2326,
                2296,
                2268,
                2240,
                2213,
                2187,
                2161,
                2136,
                2111,
                2087,
                2063,
                2040,
                2018,
                1996,
                1974,
                1953,
                1932,
                1912,
                1892,
                1873,
                1853,
                1835,
                1816,
                1799,
                1781,
                1764,
                1747,
                1730,
                1714,
                1698,
                1682,
                1667,
                1651,
                1637,
                1622,
                1608,
                1594,
                1580,
                1566,
                1553,
                1539,
                1526,
                1514,
                1501,
                1489,
                1477,
                1465,
                1453,
                1442,
                1430,
                1419,
                1408,
                15708,
                15182,
                14659,
                14142,
                13633,
                13135,
                12649,
                12178,
                11723,
                11284,
                10863,
                10460,
                10075,
                9707,
                9358,
                9025,
                8709,
                8409,
                8124,
                7854,
                7598,
                7354,
                7124,
                6904,
                6696,
                6499,
                6311,
                6132,
                5962,
                5800,
                5646,
                5499,
                5358,
                5224,
                5096,
                4973,
                4856,
                4744,
                4636,
                4533,
                4434,
                4340,
                4248,
                4161,
                4076,
                3995,
                3917,
                3842,
                3769,
                3699,
                3631,
                3566,
                3503,
                3442,
                3383,
                3326,
                3271,
                3218,
                3166,
                3115,
                3067,
                3020,
                2974,
                2929,
                2886,
                2844,
                2803,
                2763,
                2725,
                2687,
                2650,
                2615,
                2580,
                2546,
                2513,
                2481,
                2450,
                2419,
                2389,
                2360,
                2332,
                2304,
                2277,
                2250,
                2224,
                2199,
                2174,
                2150,
                2126,
                2103,
                2081,
                2058,
                2037,
                2015,
                1994,
                1974,
                1954,
                1934,
                1915,
                1896,
                1878,
                1859,
                1842,
                1824,
                1807,
                1790,
                1774,
                1757,
                1741,
                1726,
                1710,
                1695,
                1680,
                1666,
                1651,
                1637,
                1624,
                1610,
                1596,
                1583,
                1570,
                1558,
                1545,
                1533,
                1520,
                1508,
                1497,
                1485,
                15708,
                15208,
                14711,
                14219,
                13734,
                13258,
                12793,
                12341,
                11903,
                11479,
                11071,
                10680,
                10304,
                9944,
                9601,
                9273,
                8961,
                8663,
                8380,
                8110,
                7854,
                7610,
                7378,
                7157,
                6947,
                6747,
                6557,
                6375,
                6202,
                6037,
                5880,
                5730,
                5586,
                5449,
                5317,
                5191,
                5071,
                4956,
                4845,
                4739,
                4636,
                4538,
                4444,
                4354,
                4266,
                4182,
                4101,
                4023,
                3948,
                3875,
                3805,
                3737,
                3672,
                3608,
                3547,
                3488,
                3430,
                3375,
                3321,
                3268,
                3218,
                3168,
                3120,
                3074,
                3029,
                2985,
                2942,
                2901,
                2861,
                2821,
                2783,
                2746,
                2709,
                2674,
                2640,
                2606,
                2573,
                2541,
                2510,
                2480,
                2450,
                2421,
                2392,
                2365,
                2337,
                2311,
                2285,
                2260,
                2235,
                2210,
                2187,
                2163,
                2141,
                2118,
                2096,
                2075,
                2054,
                2033,
                2013,
                1993,
                1974,
                1955,
                1936,
                1918,
                1900,
                1882,
                1865,
                1848,
                1831,
                1815,
                1799,
                1783,
                1767,
                1752,
                1737,
                1722,
                1707,
                1693,
                1679,
                1665,
                1651,
                1638,
                1625,
                1612,
                1599,
                1587,
                1574,
                1562,
                15708,
                15232,
                14758,
                14289,
                13826,
                13371,
                12925,
                12490,
                12068,
                11659,
                11264,
                10883,
                10517,
                10165,
                9828,
                9505,
                9197,
                8903,
                8622,
                8354,
                8098,
                7854,
                7621,
                7400,
                7188,
                6987,
                6794,
                6610,
                6435,
                6267,
                6107,
                5954,
                5808,
                5667,
                5533,
                5404,
                5281,
                5162,
                5049,
                4939,
                4834,
                4734,
                4636,
                4543,
                4453,
                4366,
                4283,
                4202,
                4124,
                4049,
                3976,
                3906,
                3838,
                3772,
                3709,
                3647,
                3588,
                3530,
                3474,
                3419,
                3367,
                3316,
                3266,
                3218,
                3171,
                3125,
                3081,
                3037,
                2995,
                2954,
                2915,
                2876,
                2838,
                2801,
                2765,
                2730,
                2696,
                2663,
                2630,
                2598,
                2567,
                2537,
                2507,
                2478,
                2450,
                2422,
                2395,
                2368,
                2343,
                2317,
                2292,
                2268,
                2244,
                2221,
                2198,
                2176,
                2154,
                2132,
                2111,
                2090,
                2070,
                2050,
                2030,
                2011,
                1992,
                1974,
                1956,
                1938,
                1920,
                1903,
                1886,
                1870,
                1853,
                1837,
                1822,
                1806,
                1791,
                1776,
                1761,
                1747,
                1732,
                1718,
                1705,
                1691,
                1678,
                1664,
                1651,
                1639,
                15708,
                15254,
                14801,
                14353,
                13909,
                13473,
                13045,
                12627,
                12220,
                11825,
                11442,
                11071,
                10714,
                10371,
                10041,
                9724,
                9420,
                9129,
                8851,
                8584,
                8330,
                8086,
                7854,
                7632,
                7419,
                7217,
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                2856,
                2831,
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}